A Primer of Infinitesimal Analysis

A Primer of Infinitesimal Analysis PDF Author: John L. Bell
Publisher: Cambridge University Press
ISBN: 0521887186
Category : Mathematics
Languages : en
Pages : 7

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Book Description
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.

A Primer of Infinitesimal Analysis

A Primer of Infinitesimal Analysis PDF Author: John L. Bell
Publisher: Cambridge University Press
ISBN: 0521887186
Category : Mathematics
Languages : en
Pages : 7

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Book Description
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.

Infinitesimal Methods of Mathematical Analysis

Infinitesimal Methods of Mathematical Analysis PDF Author: J S Pinto
Publisher: Elsevier
ISBN: 0857099507
Category : Mathematics
Languages : en
Pages : 270

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Book Description
This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro. - Surveys modern reformulations of the infinitesimal concept with a comprehensive exposition of important and influential hyperreal numbers - Includes material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis

Infinitesimal Analysis

Infinitesimal Analysis PDF Author: E.I. Gordon
Publisher: Springer Science & Business Media
ISBN: 940170063X
Category : Mathematics
Languages : en
Pages : 435

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Book Description
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0

Non-standard Analysis

Non-standard Analysis PDF Author: Abraham Robinson
Publisher: Princeton University Press
ISBN: 1400884225
Category : Mathematics
Languages : en
Pages : 315

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Book Description
Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.

Models for Smooth Infinitesimal Analysis

Models for Smooth Infinitesimal Analysis PDF Author: Ieke Moerdijk
Publisher: Springer Science & Business Media
ISBN: 147574143X
Category : Mathematics
Languages : en
Pages : 401

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Book Description
The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology and vector bundles in the new context, the adequacy of these new spaces for analysis and geometry will be illustrated and the connection to the classical approach to C?-manifolds will be explained.

Hypermodels in Mathematical Finance

Hypermodels in Mathematical Finance PDF Author: Siu-Ah Ng
Publisher: World Scientific
ISBN: 9812564527
Category : Business & Economics
Languages : en
Pages : 313

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Book Description
At the beginning of the new millennium, two unstoppable processes aretaking place in the world: (1) globalization of the economy; (2)information revolution. As a consequence, there is greaterparticipation of the world population in capital market investment, such as bonds and stocks and their derivatives

Infinitesimal Calculus

Infinitesimal Calculus PDF Author: James M. Henle
Publisher: Courier Corporation
ISBN: 0486151018
Category : Mathematics
Languages : en
Pages : 146

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Book Description
Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.

Real Analysis Through Modern Infinitesimals

Real Analysis Through Modern Infinitesimals PDF Author: Nader Vakil
Publisher: Cambridge University Press
ISBN: 1107002028
Category : Mathematics
Languages : en
Pages : 587

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Book Description
A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.

De Motu and the Analyst

De Motu and the Analyst PDF Author: G. Berkeley
Publisher: Springer Science & Business Media
ISBN: 9401125929
Category : Computers
Languages : en
Pages : 235

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Book Description
Berkeley's philosophy has been much studied and discussed over the years, and a growing number of scholars have come to the realization that scientific and mathematical writings are an essential part of his philosophical enterprise. The aim of this volume is to present Berkeley's two most important scientific texts in a form which meets contemporary standards of scholarship while rendering them accessible to the modern reader. Although editions of both are contained in the fourth volume of the Works, these lack adequate introductions and do not provide com plete and corrected texts. The present edition contains a complete and critically established text of both De Motu and The Analyst, in addi tion to a new translation of De Motu. The introductions and notes are designed to provide the background necessary for a full understanding of Berkeley's account of science and mathematics. Although these two texts are very different, they are united by a shared a concern with the work of Newton and Leibniz. Berkeley's De Motu deals extensively with Newton's Principia and Leibniz's Specimen Dynamicum, while The Analyst critiques both Leibnizian and Newto nian mathematics. Berkeley is commonly thought of as a successor to Locke or Malebranche, but as these works show he is also a successor to Newton and Leibniz.

MATLAB Mathematical Analysis

MATLAB Mathematical Analysis PDF Author: Cesar Lopez
Publisher: Apress
ISBN: 1484203496
Category : Computers
Languages : en
Pages : 356

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Book Description
MATLAB Mathematical Analysis is a reference book that presents the techniques of mathematical analysis through examples and exercises resolved with MATLAB software. The purpose is to give you examples of the mathematical analysis functions offered by MATLAB so that you can use them in your daily work regardless of the application. The book supposes proper training in the mathematics and so presents the basic knowledge required to be able to use MATLAB for calculational or symbolic solutions to your problems for a vast amount of MATLAB functions. The book begins by introducing the reader to the use of numbers, operators, variables and functions in the MATLAB environment. Then it delves into working with complex variables. A large section is devoted to working with and developing graphical representations of curves, surfaces and volumes. MATLAB functions allow working with two-dimensional and three-dimensional graphics, statistical graphs, curves and surfaces in explicit, implicit, parametric and polar coordinates. Additional work implements twisted curves, surfaces, meshes, contours, volumes and graphical interpolation. The following part covers limits, functions, continuity and numerical and power series. Then differentiation is addressed in one and several variables including differential theorems for vector fields. Thereafter the topic of integration is handled including improper integrals, definite and indefinite integration, integration in multiple variables and multiple integrals and their applications. Differential equations are exemplified in detail, Laplace transforms, Tayor series, and the Runga-Kutta method and partial differential equations.